Area of square and rectangle

Area tells you how much space is inside a figure. Imagine you want to tile a kitchen floor – you need to know how many tiles will fit. That's exactly area.

Square units

For perimeter you used cm, m, or mm. For area, a small 2 goes on top: cm², m², mm². Read as "square centimeter", "square meter".

What does that mean? 1 cm² is a small patch 1 cm × 1 cm. When a figure has area 12 cm², it means 12 such small patches fit inside it.

Area of a square

Picture a square with side 4 cm broken into a grid of 1 cm × 1 cm patches. You get a 4 × 4 grid of 16 patches. The area is 16 cm².

The formula:

A = a · a

In words: the area of a square equals side times side.

Worked example

A square has a side of 7 m. What is its area?

Solution: A = 7 · 7 = 49 m². The area is 49 square meters.

Area of a rectangle

A rectangle works the same way – just remember the longer and shorter side are different. A 5 cm × 3 cm rectangle becomes a 5 × 3 grid, which has 15 patches. The area is 15 cm².

The formula:

A = a · b

In words: the area of a rectangle equals the product of the longer and shorter side.

Worked example

A flower box has a rectangular bottom with sides 30 cm and 20 cm. What is its area?

Solution: A = 30 · 20 = 600 cm². The area is 600 square centimeters.

Watch the units

It often happens that the sides are given in different units – say, one in cm and the other in m. In that case, convert both to the same unit first, and only then multiply. Otherwise the result is meaningless.

Common mistakes

Forgetting the square unit. Writing the result without the small 2 on top is wrong. Area is not a length.
Confusing area with perimeter. For a square with side 6 cm: perimeter is 24 cm, area is 36 cm². Two different numbers, two different units.
Adding instead of multiplying for a rectangle. Remember: area is multiplied, perimeter is added.

When a rectangle is actually a square

Just like with perimeter, a square is a special rectangle. So the formula A = a · b works for a square too – it's just that a = b, and so we write it more nicely as A = a · a.

Practice

Generator: Area of square and rectangle